Multidimensional polarization for ordinal data

• Published in: Journal of economic inequality Vol. 17; no. 3; pp. 301 - 317
• Main Authors: Kobus, Martyna, Kurek, Radosław
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2019; Springer; Springer Nature B.V
• Subjects: Analysis; Development Economics; Economic aspects; Economic Growth; Economic models; Economic research; Economics; Economics and Finance; Educational attainment; Equality; International Economics; Life satisfaction; Mathematical models; Multidimensional scaling; Polarization (Social sciences); Political Science; Public Finance; Quality of life; Social economics; United States; Polarization; Dominance; Multidimensional inequality; Ordinal data
• ISSN: 1569-1721; 1573-8701; 1573-8701
• DOI: 10.1007/s10888-018-9402-1

The dominant approach to evaluating distributional features of ordinal variables (e.g. self-reported health status) has been the Allison-Foster bipolarization ordering (henceforth AF ). It has not yet been extended to a multidimensional setting. Here we fill this gap. A multidimensional extension of the AF relation is characterized by a sequence of median-preserving spreads on each dimension and association-changing switches. This extension does not pay attention to the dimensions’ association. We then offer one that does and characterize it in terms of classes of polarization measures and welfare functions. Based on these two orderings we construct polarization indices and develop statistical inference for them. We measure bidimensional polarization in educational attainment and life satisfaction across OECD members. Dependence does not affect whether or not countries dominate each other bidimensionally.